This invention relates to a transmission apparatus for a vehicle. The apparatus is primarily intended for an all-terrain vehicle, and for other vehicles in which the ratio between the engine speed and the size of the road wheels tends towards the high-engine-speed, low-wheel-speed end of the scale. The apparatus is intended for use on vehicles of the kind in which skid-steering has traditionally been employed, including tracked vehicles, and vehicles in which a line of wheels on the right side are all chained together and a line of wheels on the left side are all chained together.